1. Field of the Invention
The subject invention relates to lasers, to their design and construction, and to their operation, and, more specifically, relates to lasers having concave end mirrors, to methods of operating same, reducing optical mode and bore interference therein, reducing their mirror tilting and bending sensitivity, and to their design, construction and structure.
2. Prior-Art Statement
The feasibility of producing laser action in a mixture of helium and neon gas was recognized some two decades ago and brought forth the first laser capable of operating continuously with very low energy inputs. In a gas laser complex physical phenomena have to interact in the gas charge in a certain manner calculated to bring forth a non-equilibrium condition characterized by the existence of a pair of energy levels of which the higher is more densely populated than the lower. In the past, literature on gas lasers has recognized the difficulty of discovering what transitions among the energy levels of a gas may be used for laser oscillations and what the optimum conditions for the excitation of these oscillations are, but has tended to represent the reproduction of a gas laser as a relatively modest task, requiring only moderate skill in optics and in vacuum technology (see Bela A. Lengyel, INTRODUCTION TO LASER PHYSICS [John Wiley and Sons, Inc., 1966] pp. 168 et seq.)
The latter assumption may have some validity in connection with low-efficiency experimental models, but so far has tended to inhibit radical progress in increasing the efficiency, broadening the utility and improving the quality of operation of commercial gas lasers. In particular, existing gas lasers are sensitive to tilting of the end mirrors and bending of the cavity. In helium-neon lasers, for example, this sensitivity increases as the diameter of the cavity is decreased in the interest of facilitating production of population inversion in the contained gas fill requisite to laser action.
A similar limitation exists with respect to the danger of substantial laser mode and bore interference. In this respect, it has to be kept in mind that effective laser action depends on a buildup of energy by repeated reflection of radiation between two end mirrors through a gas fill or other laser gain medium. In practice, there are definite ways or modes in which radiation in the gas fill or other laser gain medium can go back and forth between the end mirrors prior to escaping as a high-energy coherent beam through a predetermined one of these mirrors. In the fundamental mode, the energy distribution for the particular radiation is of a Gaussian nature, having a high intensity at the center of the mode and, graphically speaking, tapering off laterally in a bell-shaped curve. In consequence, the mode has no sharply defined width by nature. In practice, it is nevertheless customary to speak about a "width of the mode" by simply disregarding low-energy fringe areas of the Gaussian distribution.
Thus, the width of the mode is frequently defined as the diameter of the cross-section within which 86% of the energy occurs. Similar considerations apply to solid-state lasers where the mode has to pass through the confines of the solid lasing medium.
In practice, imperfect alignment or tilting of the end mirrors frequently impairs the development or maintenance of the mode. Even if a laser is in perfect condition at a certain point of time, thermal effects, occurring stresses and other operating conditions may engender an impairment of the mode during operation of the laser.
Douglas C. Sinclair, in "Choice of Mirror Curvatures for Gas Laser Cavities," APPLIED OPTICS, Vol. 3, No. 9 (September 1964), pp. 1067-71, examined alignment tolerance problems in three classes of laser cavities: the double concave cavity with end mirrors of equal concave curvature, the plano-concave or hemispherical cavity, and the concave-convex cavity. As a result of his examinations, Sinclair's article designated the near-hemispherical cavity as the easiest of all curved mirror cavities to align.
By way of background, a half-concentric or near-hemispherical cavity has a flat end mirror paired with a concave end mirror having a radius slightly greater than the length of the cavity and is also referred to as a half-concentric resonator. If the flat and concave mirrors in such a resonator are simultaneously tilted, such as through bending of the laser or of a supporting structure, the mode of the laser, that is, the way by which radiation from stimulated emission will travel back and forth between the end mirrors, shifts transversely due to the tilting of the mirrors and, moreover, is swept angularly due to the tilt of the flat mirror. The mode also shifts transversely even if only the concave mirror is tilted.
In the nearly concentric cavity, two concave mirrors have their centers of curvature lying near the center of the cavity. If the end mirrors in such nearly-concentric configuration are tilted due to bending of the gas discharge tube, then the mode of the laser shifts transversely. In consequence, the mode of the laser will be obstructed by the walls of the laser bore or confines of the lasing medium, resulting in degradation of the quality of the mode and of the light-output characteristics of the laser. The nearly-concentric configuration is especially sensitive to individual tilting of the end mirrors.
The known nearly-confocal configuration has two concave mirrors with their focal points lying near the center of the cavity or the midpoint between the two end mirrors. Since the focal length of a concave mirror is one-half its radius of curvature, the center of curvature of each mirror in the nearly-confocal configuration lies near the opposite mirror. In the book LASERS, edited by Albert K. Levine, Vol. 1 (Marcel Dekker, Inc., New York 1966), Ch. 5, "Modes in Optical Resonators," by H. Kogelnik, p. 312, the confocal geometry is designated as the easiest to align. However, with this configuration, simultaneous tilting of the end mirrors, such as due to bending of the laser or of a supporting structure, results in a strong transverse shift of the laser mode along the entire length of the cavity.
In consequence of these drawbacks, bending of the specifically mentioned and other prior-art laser structures frequently caused such interference of the mode with the edge of the laser bore or confinement of the lasing medium that the mode was severely degraded or even extinguished.
Accordingly, the prior art has developed proposals for preventing the mirrors from tilting. For instance, the laser structure and especially the parts holding the mirrors have been made as stiff as possible. In some instances, special mechanisms have been devised to isolate the mirror mounts from forces that would tilt the mirrors. Such prior art measures tend to encumber the laser structure and to add considerably to its weight and cost.
In an attempt to increase mode/bore tolerances, prior-art gas lasers exposed to bending effects or similar mirror/bore alignment problems typically have been provided with a bore that was considerably larger relative to the effective mode width than would have been ideal from the point of view of sustained population inversion generation and output/input efficiency. In addition to entailing a sacrifice in efficiency, a liberal bore width permits development of divergent modes or non-circularly-symmetrical mode/bore relationships.
In order to enable a better control over the mode, some designs have provided a bore with a carefully selected ideal diameter at one point along its length, but larger-than-ideal diameter or diameters over the remainder of the bore. Such approach, however, requires that the mode be aligned so that its cross-section is concentric with the ideal diameter exactly at the point of location of such limiting aperture. This requirement of itself introduces design limitations and still cannot remove the main disadvantage that the excessively large diameter besides the limiting aperture inevitably decreases the effectiveness of the active medium on which the optical mode feeds and thereby diminishes the strength of the mode and the light output of the laser.
In the general context of this prior-art statement, reference may be had to the article entitled "Laser Beams and Resonators" by H. Kogelnik and T. Li, in APPLIED OPTICS, Vol. 5, No. 10 (October 1966) pp. 1550 et seq. In Section 2.3 of that article, the authors deal with the stability of laser resonators and set forth the stability condition in the form of ##EQU1## wherein d=distance between end mirrors or length of resonator cavity,
R.sub.1 =radius of curvature of one end mirror, PA1 R.sub.2 =radius of curvature of the other end mirror.
In FIG. 4 of that article, the authors also supply a stability diagram in the plane 1/R.sub.1 vs. 1/R.sub.2 having a pair of white areas representing stable regions and two pairs of shaded areas indicating unstable regions. In particular, the boundary lines between the stable an unstable regions are two straight lines given by EQU d/R.sub.1 =1, d/R.sub.2 =1 (2)
and a pair of hyperbolae which satisfy EQU d=R.sub.1 +R.sub.2 ( 3)
excluding the origin d/R.sub.1 =d/R.sub.2 =0.
The mentioned FIG. 4 of the article under consideration also contains sketches of end mirror pairs with associated radii. No consideration, however, appears to be given to the subjects of reducing bending sensitivity or increasing alignment tolerance in gas lasers. Rather, different proportions of mirror radius pairs are effectively treated as equivalent in the stable regions of the mentioned diagram.
Reference may in this respect also be had to the above mentioned book entitled LASERS which on page 309 in FIG. 4 also shows the above mentioned stability diagram and elaborates on stability conditions in Section III. A. on pp. 308 et seq., giving the equation EQU 0&lt;[(d/R.sub.1)-1][(d/R.sub.2)-1]&lt;1 (4)
as an equivalent to the above mentioned stability equation (1).
Similarly, reference may be had to INTRODUCTION TO OPTICAL ELECTRONICS by Amnon Yariv (Holt, Rinehart and Winston, 2nd. ed. 1976) which on pp. 72 et seq. also shows the above mentioned stability diagram and sets forth useful information on resonator modes.
None of these references, however, offer or suggest a solution to any of the above mentioned problems.
Prevailing prior-art drawbacks and limitations have prevented widespread use of a technique which is working quite successfully in other areas; namely the technique of potting. For instance, potting of the tube or other fragile structure of a gas or similar laser could render the laser practically non-breakable or shatterproof. Potting could also eliminate undesired air convection at the laser tube and prevent a buildup of transverse temperature gradients which, in turn, would promote bending of the laser tube.
Potting moreover could protect lasers from the elements or from detrimental aspects of their environments.
So far, tubular lasers could, however, not be potted, since this in practice would lead to laser cavity bending and mirror tilting effects that impaired or inhibited laser operation.